A
tatami mat consists of a thin layer of tightly woven rushes,
on top of a coarser mat of straw bound with cords. The
upper mat is sewn to the lower one with twine. The mat
is firm but not hard.

In the United States, building dimensions
often are dictated by the size
of a standard sheet of plywood: 4 feet by 8
feet.

The sequence
in Additional Challenge 1b is aFibonacci sequence. Fibonacci was the nickname
for the Italian mathematician
Leonardo of Pisa. In his book Liber abaci,
published in 1202, Fibonacci described the following problem:

How
many pairs of rabbits can be produced from a single pair
in a year, if every month each pair bears a new pair which,
from the second month on, also becomes productive?

The resulting sequence of the pairs at the end of each
month, 1, 1, 2, 3, 5, 8, 13,
21, 34, 55,... is known as the Fibonacci sequence.